20230223, 23:27  #78 
Jun 2015
Vallejo, CA/.
2·577 Posts 

20230224, 19:41  #79 
Dec 2008
you know...around...
2^{3}×109 Posts 
SOE all over again?
Perhaps it would be expedient to consider a complete trial division sieve on large intervals in order for the search to remain exhaustive.
Not sure what's possible in terms of efficient computation, but I'm envisioning a large bitmap, for example 32 GB in size, which could contain almost 3e12 numbers if a wheel size of 30030 is used and only numbers of the form 6k+1 are being looked at (a gap of >= 1432 should appear every about 5e8 integers, only those would have to be checked again for 6k1 inbetween). To compete, we expect a throughput of at least, say, 3e10 per second. Trial division needs about 210 million primes (i.e. on top about 200 MB to store the halved differences between primes, one per byte), where I guess memory writing is the bottleneck for small primes, "mod"ing for large primes may be similarly slow (a simplification, I know, there's certainly more to it). Searching for gaps in the sieved interval is the next possible bottleneck, I don't know how much can be done in parallel. If one such interval could be dealt with in less than two minutes, we'd be happy. Is this worth any thought? What are the most critical hurdles we are facing? 
20230305, 17:14  #80 
May 2018
3·5·19 Posts 
Yes. This is a good idea. It does not seem to have any hurdles. You did primes up to 2^{64} quickly, so this should be quick, too.

20230306, 19:01  #81 
Dec 2008
you know...around...
368_{16} Posts 
Me? Not so much, my performance as a participant back in 2018 was only mediocre, remember that I didn't find any first occurrences. Unlucky me
Also I don't know how to write code comparable to that of Robert Gerbicz's. It takes way more skill and dexterity than a few lines of Pari or Basic... 
20230320, 12:30  #82 
Dec 2022
2·3^{2}·17 Posts 
The obvious question is: to what extent can that code be reused in a search beyond 2^64? Also, because of the smaller interval required (less than 2^55), it doesn't need to be as efficient.

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